The information pertaining to the relative positions of atoms near the surface of a sample is important in understanding the chemical and physical properties of surface structure. Techniques of gathering information concerning surface structure include localized source electron diffraction, such as photoelectron, Auger, and Kikuchi diffraction, low energy electron diffraction (LEED) and diffuse LEED (DLEED).
Reflected Kikuchi electrons are electrons that are back-scattered when an incident electron is directed at the surface of a sample and undergoes an inelastic collision within the sample before being scattered back out of the surface. Kikuchi electrons also typically undergo one or more elastic collisions before leaving the sample. Kikuchi electrons, whose inelastic collisions are due to thermal vibrations, have energies close to the energy of the incident electron beam because the inelastic collisions they undergo involve small energy losses.
Experiments involving Kikuchi electron diffraction patterns are generally conducted at room temperature or higher. These temperatures are necessary to provide sufficient thermal energy to cause the lattice atoms to vibrate significantly. The inelastic collision that creates a Kikuchi electron is a collision between an incident electron and a vibrating lattice atom.
Kikuchi diffraction patterns have been formed by directing a beam of incident electrons onto the surface of a sample. The intensity distribution of the diffraction pattern conveys information regarding the bonding angles of the lattice structure of the surface of the sample.
Auger electrons are also used to study lattice structures. Auger electrons are formed by a three step process involving several electrons. An incident electron strikes a "target" lattice atom and knocks an electron out of a state near the core of the target atom. The resulting core-hole is then filled by a higher energy electron near the target atom, which emits energy corresponding to the potential difference between its initial and final states. This energy is absorbed by another nearby electron, known as an Auger electron, and causes the Auger electron to be emitted from the sample.
Both Kikuchi and Auger electrons have effectively localized sources. A localized source electron is an electron that either appears to, or actually does, originate near an atomic nucleus within the sample. A Kikuchi electron is a localized source electron because phase information is lost when the electron undergoes an inelastic collision. When the phase information is lost the electron is no longer coherent with other such electrons and appears to have originated from within the sample. An Auger electron is a localized source electron because the Auger electron is not coherent with other Auger electrons.
In order to obtain three dimensional information regarding lattice structure it has been suggested to use holograms and holographic techniques (the creation of a three dimensional image from an interference pattern). A hologram is a record of an interference pattern, which, when properly illuminated, forms a three dimensional image of the object originally used to create the interference pattern. Thus, assuming that it is possible to create one, a hologram of a surface may be used to determine the relative positions of the atoms near the surface of the sample.
A hologram of an object is created by simultaneously irradiating photographic film and the object with coherent light. Light that is reflected off of the object, called the object wave, travels to the film and forms an interference pattern with the mutually coherent light that travels directly to the film (called the reference wave). When the recorded interference pattern, or hologram, is illuminated by a coherent reconstructing wave identical to the reference wave, a portion of the transmitted light (wave pattern) is identical to the light (wave pattern) that was reflected off of the object and used to create the hologram. Since this part of the transmitted wave pattern is identical to the original wave pattern, an observer at any location sees a three dimensional image of the object, just as the original object would have been seen from that location.
Electron holography is similar to conventional holography, except that the waves used to create the interference pattern are electrons. As is well known to those skilled in the art, electrons that are monochromatic (i.e. electrons that have the same energy), and that travel in the same direction (i.e. parallel to one another) may be treated as coherent waves according to theory of quantum mechanics. As the electrons become less monochromatic and/or the direction of travel of individual electrons diverges, the electron beam becomes less coherent. Thus, when electrons having an appropriate uniformity of energy and direction of travel to be considered coherent waves over the distance travelled from the object to the holographic film are utilized, a recorded interference pattern between an electron reference wave and an electron object wave form a hologram. The hologram, when illuminated by a reconstructing electron wave identical to the reference wave, should produce a three dimensional image.
The use of electron holography to gather information concerning surface structure promises to be a great advance in the art. It has been suggested, for example, that, an electron hologram can be created by recording the intensity of an interference pattern formed by electrons which are emitted from an adsorbed atom, and travel to the film directly from the adsorbed atom (the reference wave), or after scattering off of one or more nearby substrate atoms (the object wave). Then, rather than physically illuminating the hologram to reconstruct the image, data corresponding to the reconstructed intensity is generated by multiplying the recorded data by a function representing the intensity of a reconstructing wave, i.e. "mathematically" illuminating the hologram to reconstruct a real image. The image intensity at points off the hologram, i.e. a reconstructed image, may then be appropriately determined via a computer using certain mathematical techniques.
One method of using holographic techniques to determine surface structure is set forth in Photoelectron Holography. Vol. 61, No. 12, Phys. Rev. Letters, Sep. 19, 1988, by John Barton, which proposed to interpret photoelectron (PhD) data, collected on a portion of a spherical surface centered about a crystal having adsorbed atoms, as a photoelectron hologram. It was suggested that the photoelectron data may be normalized by subtracting from each intensity data point the intensity of the reference wave, and then dividing this difference by the square root of the intensity of the reference wave. Next, the normalized data, which corresponds to the intensity of a hologram (film), is then multiplied by a function representing a reconstructing wave, which is the conjugate of the reference wave, in this case a converging spherical wave. The resultant data corresponds to the transmitted intensity of an illuminating wave. The intensity at points off of the hologram (the spherical surface) is calculated using a mathematical technique called the Helmholtz-Kirchoff integral.
The Helmholtz-Kirchoff integral is a well known technique of determining the intensity of light in three dimensions given the intensity on a surface, and is particularly useful in PhD applications. According to the Helmholtz-Kirchoff integral, each point on the surface is treated as a point source of light, and a mathematical expression for the intensity in three dimensions due to each individual point source is determined. A mathematical expression for the total intensity in three dimensions is simply the sum of the amplitudes due to the point sources, and may be found by integrating the function representing the amplitudes due to the individual point sources over the surface (i.e. the point sources). The Helmholtz-Kirchoff integral, when applied to PhD holographic data, is in the form of a double Fourier integral, and may be solved numerically using a fast Fourier transform.
Another method of obtaining surface structure information is a technique of using low energy electrons to form a diffraction pattern (LEED). LEED involves scattering approximately 20-500 eV electrons off of a crystalline structure, thereby forming a diffraction pattern comprised of Bragg spots (i.e., concentrated high intensity areas) with low intensity areas between. The low energy ensures that the electrons penetrate only a few atomic layers of the substrate.
Experiments involving LEED have been used to determine surface structure. For example, using LEED with crystals assumed to have perfect order (i.e. no adsorbed atoms with the crystal being periodic in all directions), the relative intensities of the various Bragg beams are measured, from which surface structure information is calculated. When partial disorder is assumed, i.e., when the surface is periodic in at least one direction and non-periodic in at least one direction, the disorder is reflected in and calculated from the intensity distributions within a Bragg beam (beam profiles).
Other prior art methods utilize diffuse LEED (DLEED) intensities (the intensities between Bragg beams) to determine surface structure of crystals having no long range order, such as a crystal having adsorbed atoms located randomly throughout the surface, though with locally identical environments as is often the case. For example, Measurement of Diffuse LEED Intensities, Surface Science Vol. 173, No. 2-3, pp. 366-378, Heinz et al., describes a method to determine the local environment of the adsorbed atoms. Such method includes the repetitive measurement of diffuse LEED intensities from crystals having adsorbed atoms and then calculating a smoothed spatial diffuse intensity distribution. The experimentally obtained distribution is then compared to computer generated distributions based on model crystal surface structures. When a computer generated distribution corresponds closely to the experimentally obtained distribution the conclusion is drawn that the surface structure of the experimental crystal is closely related to that model surface structure.
One overwhelming disadvantage of the prior art DLEED technique is that generation of the theoretical data is too time consuming to be performed concurrently with the experiment, but rather requires hours of super computer CPU time. The significant time involved in making the calculations and high cost of using super computer time presently makes it expensive and inefficient to use DLEED for gathering information concerning surface structure of crystalline material. Another disadvantage of all DLEED experiments is that they must be conducted at extremely low temperatures, near 77K. Finally, both DLEED and LEED techniques are directed to determining the local environment of an adsorbed atom, not a substrate atom.
Accordingly, a practical and inexpensive method and apparatus of determining the surface structure of ordered atoms near the surface of a sample which is capable of conveying the structure as the experiment is being performed is highly desirable. Furthermore, such a system would preferably be one which utilizes a source of electrons readily available in most laboratories, and be capable of being performed at room temperature.